Abstract:
In the rectangular region, we study nonlocal boundary value problems for the one-dimensional unsteady convection-diffusion equation of fractional order with variable coefficients, describing the diffusion transfer of a substance, as well as the transfer due to the motion of the medium. A priori estimates of solutions of nonlocal boundary value problems in differential form are derived by the method of energy inequalities. Difference schemes are constructed and analogs of a priori estimates in the difference form are proved for them, error estimates are given under the assumption of sufficient smoothness of solutions of equations. From the obtained a priori estimates, the uniqueness and stability of the solution from the initial data and the right part, as well as the convergence of the solution of the difference problem to the solution of the corresponding differential problem at the rate of O(h2+τ2).
Keywords:
nonlocal boundary value problems, a priori estimate, nonstationary convection-diffusion equation, fractional order differential equation, fractional Caputo derivative.
Citation:
M. Kh. Beshtokov, V. A. Vogahova, “Nonlocal boundary value problems for a fractional-order convection-diffusion equation”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:4 (2019), 459–482
\Bibitem{BesVog19}
\by M.~Kh.~Beshtokov, V.~A.~Vogahova
\paper Nonlocal boundary value problems for a fractional-order convection-diffusion equation
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2019
\vol 29
\issue 4
\pages 459--482
\mathnet{http://mi.mathnet.ru/vuu695}
\crossref{https://doi.org/10.20537/vm190401}
Linking options:
https://www.mathnet.ru/eng/vuu695
https://www.mathnet.ru/eng/vuu/v29/i4/p459
This publication is cited in the following 9 articles:
Z. V. Beshtokova, “Finite Difference Method for Solving Parabolic-Type Integro-Differential Equations in Multidimensional Domain with Nonhomogeneous First-Order Boundary Conditions”, CMIT, 8:1 (2024), 43
M. Kh. Beshtokov, “Initial-Boundary Value Problems for the Moisture Transfer Equation with Different Order Fractional Derivatives and Nonlocal Linear Source”, Sib Math J, 65:6 (2024), 1407
Z. V. Beshtokova, “Konechno-raznostnye metody resheniya nelokalnoi kraevoi zadachi dlya mnogomernogo parabolicheskogo uravneniya s granichnymi usloviyami integralnogo vida”, Dalnevost. matem. zhurn., 22:1 (2022), 3–27
Z. V. Beshtokova, M. Kh. Beshtokov, M. Kh. Shkhanukov-Lafishev, “Ob odnoi raznostnoi skheme resheniya zadachi Dirikhle dlya mnogomernogo uravneniya diffuzii s drobnoi proizvodnoi Kaputo v oblasti s proizvolnoi granitsei”, Vladikavk. matem. zhurn., 24:3 (2022), 37–54
M. Kh. Beshtokov, “Kraevye zadachi dlya uravneniya sobolevskogo tipa drobnogo poryadka c effektom pamyati”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 26:4 (2022), 607–629
M. Kh. Beshtokov, M. Z. Khudalov, “Raznostnye metody resheniya nelokalnykh kraevykh zadach dlya differentsialnykh uravnenii konvektsii-diffuzii drobnogo poryadka c effektom pamyati”, Dalnevost. matem. zhurn., 21:1 (2021), 3–25
M. Kh. Beshtokov, Z. V. Beshtokova, “Metod setok priblizhennogo resheniya nachalno-kraevykh zadach dlya obobschennykh uravnenii konvektsii-diffuzii”, Vladikavk. matem. zhurn., 23:3 (2021), 28–44
A. A. Alikhanov, M. KH. Beshtokov, M. H. Shhanukov-Lafishev, “Local one-dimensional scheme for the first initial-boundary value problem for the multidimensional fractional-order convection–diffusion equation”, Comput. Math. Math. Phys., 61:7 (2021), 1075–1093
M. Kh. Beshtokov, Z. V. Beshtokova, M. Z. Khudalov, “Konechno-raznostnyi metod resheniya nelokalnoi kraevoi zadachi dlya nagruzhennogo uravneniya teploprovodnosti drobnogo poryadka”, Vladikavk. matem. zhurn., 22:4 (2020), 45–57
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